New electronic components

[Subhendu Das]

Can we make new electronic components?

Capacitors and Inductors are based on the following concepts of
calculus.

Is calculus continuous or discrete? Consider the Derivative operator
D[x^n]. It produces nx^(n-1). Is this a continuous operation? No. If
you plot the graphs of x^n and nx^(n-1), you will see a large gap
between them. The Derivative operator D peels off a function in
discrete steps.

One would like to have a Derivative that would behave like a
continuous operator. As an example, consider an operator a-Derivative
with the definition A[x^n] = nx^(n-a). Here a is a real number between
0 and 1. This a-Derivative will fill up the gap between the two
functions. We can now smoothly change a to smoothly peel the original
function.

If we can create capacitors and inductors that will follow the
a-Derivative, then we may see a completely different technology.

Please send your comments to subhendu.das@excite.com

 

[Aaron Hughes]

Strange proposal, but here are my thoughts.

To say that Capacitors and Inductors are based on calculus is true.
BUT it is more correct to say that Calculus is based on Capacitors and
Inductors.

Nobody wanted to try and build an electronic component to model a math
equation,
instead it was the other way around. The question asked was most likely,
"these caps and inductors we use all the time, I wonder if I can describe
them mathematically?"
Don't forget that math is not just a torture device, but a useful tool to
attempt
to describe before hand, what circuits will do in the lab. That is how
Workbench and Spice work.

Finally your A[x^n] = nx^(n-a) idea. Well this has been made, just not in
one component as you suggest.
An RLC circuit could make this device, or opamps, or even some type of
digital circuit. With some
simplification you get
A[x^n] = nx^(n-a) = n(x^n)(x^-a) = n(x^n) / (x^a)

Nevertheless, I do see your point about smoothly getting the derivative.
What sort of application do you think this would have?


--
Aaron Hughes
http://www.canerdian.ca
"Subhendu Das" <subhendu.das@excite.com> wrote in message
news:e9778353.0403261450.14167cf7@posting.google.com...

Can we make new electronic components?

Capacitors and Inductors are based on the following concepts of
calculus.

Is calculus continuous or discrete? Consider the Derivative operator
D[x^n]. It produces nx^(n-1). Is this a continuous operation? No. If
you plot the graphs of x^n and nx^(n-1), you will see a large gap
between them. The Derivative operator D peels off a function in
discrete steps.

One would like to have a Derivative that would behave like a
continuous operator. As an example, consider an operator a-Derivative
with the definition A[x^n] = nx^(n-a). Here a is a real number between
0 and 1. This a-Derivative will fill up the gap between the two
functions. We can now smoothly change a to smoothly peel the original
function.

If we can create capacitors and inductors that will follow the
a-Derivative, then we may see a completely different technology.

Please send your comments to subhendu.das@excite.com

 

[Subhendu Das]

Thank you Aron for your comments. I am glad to see that you have
realized that calculus is not smooth enough. I want somebody to do
something about it.


If we use this calculus then we will not be able to describe our
nature adequately. Only a continuous system can answer questions like
"Is nature continuos or discrete?" If you put an oscilloscope probe on
a pin of any digital circuit then you will see a continuous signal.
Thus digital circuits, in reality, are continuous systems. We can see
this because the scope is a continuous system. If calculus is discrete
then we have a wrong mathematical tool for investigating our physics.


I want to make a three or two terminal component that will follow the
a-Derivative formula. One of the terminals will supply the value for
"a or alpha" or it may be two terminal component with a fixed and
predefined value for a. Once we make these components then we can see
how a complete circuit (like RLC) behaves with these new components.
We may see something amazing and new applications will follow.


These days we try to make capacitors and inductors to behave like
sinusoidal components. That is when we apply a precise sinusoidal
input signal we like them to produce very precise sinusoidal output
signal. That defines the quality of the component. That is we try to
make them follow Newtonian derivative. I want to see if we can make
components to follow alpha-Derivative that I have described.

Please send your comments to: subhendu.das@excite.com



"Aaron Hughes" <urpNOSPAM@canerdian.ca> wrote in message news:<nZg9c.22713$QO2.15121@pd7tw1no>...

Strange proposal, but here are my thoughts.

To say that Capacitors and Inductors are based on calculus is true.
BUT it is more correct to say that Calculus is based on Capacitors and
Inductors.

Nobody wanted to try and build an electronic component to model a math
equation,
instead it was the other way around. The question asked was most likely,
"these caps and inductors we use all the time, I wonder if I can describe
them mathematically?"
Don't forget that math is not just a torture device, but a useful tool to
attempt
to describe before hand, what circuits will do in the lab. That is how
Workbench and Spice work.

Finally your A[x^n] = nx^(n-a) idea. Well this has been made, just not in
one component as you suggest.
An RLC circuit could make this device, or opamps, or even some type of
digital circuit. With some
simplification you get
A[x^n] = nx^(n-a) = n(x^n)(x^-a) = n(x^n) / (x^a)

Nevertheless, I do see your point about smoothly getting the derivative.
What sort of application do you think this would have?


--
Aaron Hughes
http://www.canerdian.ca
"Subhendu Das" <subhendu.das@excite.com> wrote in message
news:e9778353.0403261450.14167cf7@posting.google.com...
Can we make new electronic components?

Capacitors and Inductors are based on the following concepts of
calculus.

Is calculus continuous or discrete? Consider the Derivative operator
D[x^n]. It produces nx^(n-1). Is this a continuous operation? No. If
you plot the graphs of x^n and nx^(n-1), you will see a large gap
between them. The Derivative operator D peels off a function in
discrete steps.

One would like to have a Derivative that would behave like a
continuous operator. As an example, consider an operator a-Derivative
with the definition A[x^n] = nx^(n-a). Here a is a real number between
0 and 1. This a-Derivative will fill up the gap between the two
functions. We can now smoothly change a to smoothly peel the original
function.

If we can create capacitors and inductors that will follow the
a-Derivative, then we may see a completely different technology.

Please send your comments to subhendu.das@excite.com

 

[Subhendu Das]

Thank you Aron for your comments. I am glad to see that you have
realized that calculus is not smooth enough. I want somebody to do
something about it.


If we use this calculus then we will not be able to describe our
nature adequately. Only a continuous system can answer questions like
"Is nature continuos or discrete?" If you put an oscilloscope probe on
a pin of any digital circuit then you will see a continuous signal.
Thus digital circuits, in reality, are continuous systems. We can see
this because the scope is a continuous system. If calculus is discrete
then we have a wrong mathematical tool for investigating our physics.


I want to make a three or two terminal component that will follow the
a-Derivative formula. One of the terminals will supply the value for
"a or alpha" or it may be two terminal component with a fixed and
predefined value for a. Once we make these components then we can see
how a complete circuit (like RLC) behaves with these new components.
We may see something amazing and new applications will follow.


These days we try to make capacitors and inductors to behave like
sinusoidal components. That is when we apply a precise sinusoidal
input signal we like them to produce very precise sinusoidal output
signal. That defines the quality of the component. That is we try to
make them follow Newtonian derivative. I want to see if we can make
components to follow alpha-Derivative that I have described.